Week 1
Anxiety disorders are the most commonly diagnosed disorders in children and adolescents. Fortunately, recent research suggests that many youths with anxiety disorders can be treated using cognitive behavioral therapy (CBT). In the past, anxiety disorders were traditionally treated with either psychodynamic therapy or a supportive type of therapy (one that offers encouragement and empathy but is not really driven by any particular theory of psychotherapy). Therefore, it is important to know how the CBT compares to these types of treatments. Your job is to use a dataset to conduct the types of analyses (both descriptive and inferential) that would be included in a research report addressing this dataset.
In this course, you will use a dataset similar to the one psychologists use when conducting this type of research. You will write sections of a research report (the results section, a brief discussion section, and part of the methods section) using the APA format.
The researchers conducting the study measured children’s anxiety before and after treatment using the Revised Children’s Manifest Anxiety Scale (RCMAS), a
self-report of anxiety in which scores can range from 0–28 (with higher scores indicating higher anxiety). Researchers also measured the related constructs of depression and self-efficacy for dealing with anxiety provoking situations (both measured on a scale of 0–10 with higher scores indicating more depression and higher self-efficacy) both before and after the treatment. The researchers also defined recovery as a decrease to a score of less than 5 on the RCMAS posttreatment. This variable is not in the database. You will need to create it. Of course, the researchers also kept track of which children received which treatment. The children also provided their age, sex, and ethnicity.
Week 2
Choose and compute the appropriate descriptive statistics to describe the characteristics of the sample under study (sex distribution, age, and ethnicity) and the anxiety reported by the sample, making sure to include at least one example of each:
- A visual descriptive
- A measure of central tendency
- Variability
Week 3
What score on the pretreatment Revised Children's Manifest Anxiety Scale (RCMAS) would correspond to an extremely high score?
X=(Z)(SD) + M
X= (1.64)(3.740) + 20.22 = 6.1336 + 20.22 = 26.3536 = 26
An extreme high score on the pretreatment RCMAs would be 26 or higher.
What score on the pretreatment RCMAS would correspond to an extremely low score?
X=(Z)(SD) + M
X=(-1.64)(3.740) + 20.22 = -6.1336 + 20.22 = 14.0864 = 14
An extreme low score on the pretreatment RCMAs would be 14 or lower.
Subject ID / Pretreatment RMCS / Z-Score5 / 20 / -.05941
10 / 28 / 2.07937
15 / 24 / 1.00998
20 / 28 / 2.07937
25 / 17 / -.86145
Week 4
Overview week nothing new
Week 5
(a) This will be a two-tailed test
Two-tailed because here, the null hypothesis would be thatμ1 =μ2 =μ3, and the alternative would be thatμ1≠μ2≠μ3. Thus, we are testing to see if the means are all the sameor are theydifferent more or less. Hence two-tailed.
(2) Type I error: Concluding on the basis of the test that the three treatments differ in how well they work, whereas in reality they do not differ
Type II error: Failing to conclude on the basis of the test that the three treatments differ in how well they work, whereas in reality they do differ
(1) This will be a one-tailed test
One-tailed because here, the null hypothesis would be thatμ2 =μ1, and the alternative would be thatμ2 < μ1. Thus, we are testing to see if the children fare thesameor do they fareworseless. Hence one-tailed.
(2) Type I error: Concluding on the basis of the test that children receiving therapy will get worse over time, whereas in reality they do not
Type II error: Failing to conclude on the basis of the test that children receiving therapy will get worse over time, whereas in reality they do
(1) This will be a one-tailed test
One-tailed because here, the null hypothesis would be thatμ(females) =μ(males), and the alternative would be thatμ(females) > μ(males). Thus, we are testing to see if females do thesameor do they dobetter(more).Hence one-tailed.
(2) Type I error: Concluding (on the basis of the test) that girls will do better than boys, whereas in reality they are no such indications
Type II error: Failing to conclude on the basis of the test that girls will do better than boys, whereas in reality they do better.
Week 6
Part 1
Group Statistics
RCMAS post treatment
CBTNMeanStd. DeviationStd error Mean
337.39394.34410.75621
PSY3311.78793.79768.66109
Independent Sample Test
RCMAS Post Treatment
Equal variances assumed
F=.881
Sig=.351
T=4.375
Df=64
Sig(2 tailed)=.000
Mean diffrence=-4.39394
Std error diffrence=1.00444
95% confidence interval of the diffrence
lower=-6.40054
upper=-2.38734
Equal variance no assumed
T=4.375
Df=62.877
Sig (2 tailed)= .000
Mean diffrence= -4.39394
Std Error Diffrence= 1.00444
96% confidence interval of the diffrence
lower= -6.40123
upper=-2.38665
The test to be used is independent samples t test for equality of means.
The computed value of test statistic is
Degrees of freedom = 64
The p-value is 0.000
Since the t is highly significant, we reject the null hypothesis and conclude that the post treatment RCMAS of CBT and PSY are not the same.
Part 2
Paried sample statistics
CBT Pretreatment
Mean= 20.3333
N=33
St deviaton=3.70529
Std error mean=.64501
CBT post treatment
Mean=7.3939
N=33
Std deviation=4.34410
Std.error mean=.75621
Paired Sample Correlations
CBT Pretreatment and post treatment
N=33
Correlation=.174
Sig=.333
Paired Sample Test
CBT Pretreatment and posttreatment
Mean 1.29394
St Deviation=5.19579
Std Error Mean=.90447
95% confidence interval of the diffrence
lower= 11.09705
upper=14.78174
t=14.306
df=32
sig (2tailed)=.000
The test to be used is the paired t test for equality of means.
The computed value of test statistic is
Degrees of freedom = 32
The p-value is 0.000
Since the t is highly significant, we reject the null hypothesis and conclude that the mean pre treatment RCMAS of CBT and the mean post treatment RCMAS of CBT are not the same.
Analysis
In part1 we compared the RCMAS post treatment scores of CBT and PSY. The sample means are 7.3939 and 11.7879. The difference is found to statistically significant. So we conclude that the post treatment RCMAS scores of CBT and PSY are not the same. In fact the post treatment scores of PSY are significantly greater than the post treatment scores of CBT.
In part2 we compared the pre treatment and post treatment RCMAS scores for CBT. The sample means are 20.3333 and 7.3939. The difference is found to be statistically significant. So we conclude that the pretreatment and post treatment scores are not the same. In fact the post treatment scores of CBT is significantly less than the pretreatment scores.
Week 7
Analysis of variance (ANOVA) comparing anxiety levels of participants across three treatment conditions.
The null hypothesis to be tested is that the post anxiety levels are the same for all the three treatments. The alternative hypothesis is that they are not all the same.
SUMMARYGroups / Count / Sum / Average / Variance
CBT / 33 / 244 / 7.393939 / 18.8712
PSY / 33 / 389 / 11.78788 / 14.4223
SUPP / 33 / 531 / 16.09091 / 15.7727
ANOVA
Source of Variation / SS / df / MS / F / P-value / F crit
Between Groups / 1248.0606 / 2 / 624.030303 / 38.1543 / 6.4E-13 / 3.091191
Within Groups / 1570.1212 / 96 / 16.35542929
Total / 2818.1818 / 98
The Computed F statistic is 38.1543. It is significant at the 5% level of significance. The p-value of the test is 6.4E-13. So the post test anxiety levels of the three treatments are not the same.
Post hoc tests
The least significant difference is 1.9763. The difference between the sample means for the three treatments taken in pairs are 4.3939, 8.6970 and 4.3030. All these are greater than the LSD 1.9763.
So the post test anxiety levels of the three groups are different.
So from post hoc analysis we conclude that the post test anxiety levels of the three treatments taken in pairs is different for each pair.
Analysis of variance (ANOVA) comparing anxiety levels of participants across three treatment conditions.The null hypothesis to be tested is that the post anxiety levels are the same for all the three treatments. The alternative hypothesis is that they are not all the same.
Week 8
Interpretation
The model fitted is a two way analysis of variance with interaction.
The treatment sum of squares is 1178.652 on 2 df. The mean square is 589.326. The F statistic for testing whether there is difference between the mean scores for the treatments is 36.422. The p-value is 0.000 which is less than the significance level 0.05. So we conclude that the mean post treatment RCMAS scores for the three treatments are not the same.
The sum of squares due to sex is 38.572 on 1 df. The mean square is 38.575 and the F is 2.384. The p-value is .126. It is less not less than 0.05. So we conclude that the mean post treatment RCMAS scores for Males and females are the same.
The sum of squares for the interaction between treatment and sex is 82.693 on 2 df. The mean square is 41.347 and the F is 2.599. The p-value is 0.080 which is not less than 0.05 and we conclude that there is no interaction between sex and treatment.
Conclusions
We conclude that
(1)There is difference between the mean post treatment RCMAS scores across treatment conditions.
(2)There is no difference between the mean post treatment RCMAS scores across sex.
(3)There is no interaction effect between treatment conditions and sex.
Post HOC test
The difference between the mean post treatment RCMAS scores for CBT and PSY is 4.39 and is significant at the 5% level of significance.
The difference between the mean post treatment RCMAS scores for CBT and SUPP is 8.69 and is significant at the 5% level of significance.
The difference between the mean post treatment RCMAS scores for PSY and SUPP is 4.30 and is significant at the 5% level of significance.
Conclusion
The difference between the mean post treatment RCMAS scores between the treatment conditions considered in pairs are all significantly different.
Week 9
Mauchly's Test of Sphericity doesn’t generate a p-value as there are only two within-subject factors - Pre-treatment and Post-treatment RCMAS so that df=0. But a look at the chi-square value (x² = 0.000) and epsilon (ε=1) indicate the assumption of sphericity is exactly satisfied.
In table for within-subject effects, assuming sphericity, Anxiety Level has a significant effect on RCMAS (F=407.585, p=0.000). Also, there is a significant interaction between anxiety levels and the treatment conditions (F=35.278, p=0.000). This means, not only do RCMAS scores have changed after treatment, but various treatment conditions have caused different impact on the scores after treatment. Thus, the methods have been effective in treating anxiety.
Week 10
SPSS output
CorrelationsRCMAS-Pretreatmnet / Depression-Pretreatment
RCMAS-Pretreatmnet / Pearson Correlation / 1 / .130
Sig. (2-tailed) / .199
N / 99 / 99
Depression-Pretreatment / Pearson Correlation / .130 / 1
Sig. (2-tailed) / .199
N / 99 / 99
Interpretation
Pearson’s correlation coefficient between pre-treatment anxiety and depression scores is 0.130. Thus, there is very weak positive relationship between the two variables. Significance test for the correlation coefficient gives a p-value of 0.199 which indicates that the relationship isn’t statistically significant, as p-value is more than the customary significance level 0.05. Thus, there isn’t enough evidence to say that children who reported severe anxiety also had reports of high depression, or vice versa.